If an initial principal P is invested at an annual rate r an

If an initial principal P is invested at an annual rate r and the interest is compounded n times per year, the amount A in the account after t years is A = p(1 + r/n)^nt. On May 31, 2009, the Annual Percentage Rate listed at Jeff\'s bank for regular savings accounts was 0.35% compounded monthly. Use the equation above to answer the following. If P = 4000 what is A(9)? (Round your answer to the nearest cent.) Using the principal from part (a), solve the equation A(t) = 8000 for t. (Round your answer to two decimal places.) What principal P should be invested so that the account balance is $3000 in three years? (Round your answer to the nearest cent.) P = $ 2154.5 A finance company offers a promotion on $5000 loans. The borrower does not have to make any payments for the first two years, however interest will continue to be charged to the loan at 29.2% compounded continue are made? (Round your answer to the nearest cent.) If the promotion is extended an additional two years, and no payments are made, what amount would be due? (Round your answer to the nearest cent.)

Solution

A(t) = P(1 +r/n)^nt

a) A(9) = 4000( 1 +0.0035/12)^12*9 = 4000*1.031 = $ 4127.99

b) A(t) = 8000 find t:

8000 =4000(1.00029)^12t

2 = (1.00029)^12t

take log on both sided:

ln2 = 12t*ln(1.00029)

t = 199.21 years

c) 3000 =P( 1+0.0035/12)^36

   3000 = P(1.01055)

P = $ 2968.68